A typical problem involving the area and perimeter of a parallelogram gives us the area, perimeter and/or base, height, and an angle of the parallelogram. We may also be given a relationship between the area and perimeter or between the base and height of the parallelogram. We need to calculate some of these quantities given information about the others. Two examples of this type of problem follow:

Notice that s1 > s2. These parallelograms show two of the infinitely many possible parallelograms with a base of 8 and a height of 4.

We can find the area of these parallelograms by using A = bh = (8)(4) = 32. We can NOT find the perimeter because there are infinitely many possible parallelograms that can drawn having different lengths for the other two sides.

Notice the importance of making a diagram (or more than one) to see what is happening when using the given information.

This type of problem involves relationships among the lengths of the sides and height as well as the area and perimeter of a parallelogram. We need to focus on two formulas: (1) area which requires a measurement of the base and height, which we call h and (2) the perimeter which is the sum of all four sides. Sometimes it is useful to remember that the opposite sides of a parallelogram are always equal. Sometimes an angle of the parallelogram is also given so that we can use one of the basic trigonometric ratios of sine, cosine, or tangent to calculate the length of the height.

Sometimes there is not enough information given to find the perimeter. While the base and height do determine the area, there are infinitely many parallelograms with the same base and height, but different perimeters.